[r-t] Scientific triples

[Wyld Family e-mail]

I don't think there is anything inherently spliceable about methods based on
the same mathematics as Scientific however I can suggest a few
possibilities: -

It may be possible to generate three ten change (or five six change) methods
which together generate each of the cosets corresponding to the thirty
changes in the lead of Scientific.  The 24 courses of each of these three
methods would contain different changes and if joined together would
generate a peal.  Whether this is actually feasible I haven't tried to find
out.

Course splices are possible.  I know of two different methods which contain
exactly the same changes.  Neither is very exciting indeed one is the seven
part touch of original triples that was probably John Carter's starting
point.  More practically every assymetric method may be spliceable with its
inverse i.e. the method rung backwards.  To achieve this it is necessary to
use a double.  Starting with Scientific I have called the inverse
New-Scientific (on the same basis that Grandsire rung backwards is New
Grandsire) but if anyone rings it they can of course choose their own name.
The place notation is: -

1.7.1.7.1.7.1.5.1.5.1.7.1.7.1.7.1.7.1.5.7.1.7.1.5.1.7.1.3.7

The double is called at either lead end and the place notation is 347
replacing the final 7ths place.  It is possible to have the call and change
of method at another point in the lead so that it is not necessary for a
bell to ring for 4 blows in the same position but for this example I have
stuck to calls and changes of method at the lead end although that means 4
blows in 3rds when the change is from New-Scientific to Scientific.
Whenever a double is called there is a change of method and whenever there
is a change of method there must be a double.  The first composition is a
regular 7 part.  This has more changes of method than the bare minimum but
since a regular 7 part of Scientific (or any other method based on the same
mathmatics) is impossible without the use of the call that affects all 7
bells (5.1.5 becomes 5.7.5) I thought it would be interesting.  I have only
listed the methods since every change coincides with a double.

S, 2N, 3S, N, 4S, 2N, 5S, N, 2S, 3N (there is a call at the part end so that
the next part can start with Scientific)   Part end 5362714

For those looking for more changes of method, and something more challenging
to call, the following has two changes of method fewer than the maximum.  I
could not resist the temptation to produce a palindromic composition which
entailed splitting a block into two losing the two changes of method.  The
basic block is made up of 8 leads with calls and changes of method at every
lead end.  To save space I have only shown the number of lead ends to the
next plain lead end without a change of method so 1 means a plain lead
immediately and 2 means one call followed by a plain lead.  All sequences of
calls are an odd number.  Because of this plain leads alternate between
Scientific and New-Scientific (except for the 8 occasions where there are 2
plains together).

1,2,8,2,8,2,8,2,1,2,8,2,8,4,1,2,8,2,4,4,1,8,1,2,8,4,8,2,1,8,1,4,4,2,8,2,1,4,8,2,8,2

I originally sent the compositions above in February but for technical 
reasons
at this end it did not get through.  Since then I have produced two more 
compositions
based on combinations of 12 lead, 4 lead, 3 lead and 2 lead splices.  I 
haven't worked
out the specific arrangements but there is the potential for 40+ methods. 
The second
has no calls except changes of method and triple changes throughout.  I will 
submit
these when I can get the formatting sorted out.

Thanks Philip for an interesting idea.

Colin Wyld

----- Original Message ----- 
From: "Philip Earis" <pje24 at cantab.net>
To: <ringing-theory at bellringers.net>
Sent: Tuesday, January 27, 2009 10:02 PM
Subject: Re: [r-t] Scientific triples


> Further to my previous email, I'm still waiting.  Can anybody come up with 
> an interesting composition of spliced involving the "scientific" group of 
> order 168? Please?!
>
>
>
> ----- Original Message ----- 
> From: Philip Earis
> To: ringing theory
> Sent: Monday, January 05, 2009 11:44 PM
> Subject: [r-t] Scientific triples
>
>
> Yesterday I had the pleasure of ringing some scientific triples for the
> first time (http://www.campanophile.co.uk/show.aspx?Code=76703)
>
> Scientific is a well-known but rarely rung asymmetric principle with 30 
> rows
> per division:
>
> 3.1.7.1.5.1.7.1.7.5.1.7.1.7.1.7.1.7.1.5.1.5.1.7.1.7.1.7.1.7
>
> As Brian Price explains in his interesting paper published on the webpage
> www.ringing.info/bdp/triples-principles.html, Scientific "...makes use of 
> a
> group of order 168, which is well-known to mathematicians and may be used 
> to
> marshall the 5,040 Triples rows into 30 sets of 168. A principle such as
> Scientific must have a 7-part plain course of 7 x 30 rows, each section of
> 30 containing one from each set. The 7-part course makes use of the fact
> that the group contains 7-part transpositions; there will be 24 mutually
> true courses".
>
> I vaguely recall Eddie Martin once saying he had composed a similar
> companion method he intended to call "artistic" triples or something
> similar.  Is this correct?  What is the notation?
>
> Brian goes on to list the 229 principles that make use of this group with
> 7-lead courses and which have conventional symmetry. 6 of these 
> additionally
> have double symmetry, whilst 23 of these are "pure triples".
>
> I'm interested in how this concept can be taken further.  Can some of 
> these
> methods be spliced together to create a clever and challenging extent? How
> about splicing scientific with it's reverse or something similar?  What's
> possible here?
>
>
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